{"id":"https://openalex.org/W2918340795","doi":"https://doi.org/10.1109/tit.2019.2903129","title":"On the Uniqueness Result of Theorem 6 in \u201cRelative Entropy and the Multivariable Multidimensional Moment Problem\u201d","display_name":"On the Uniqueness Result of Theorem 6 in \u201cRelative Entropy and the Multivariable Multidimensional Moment Problem\u201d","publication_year":2019,"publication_date":"2019-03-05","ids":{"openalex":"https://openalex.org/W2918340795","doi":"https://doi.org/10.1109/tit.2019.2903129","mag":"2918340795"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2019.2903129","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2019.2903129","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1805.12060","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Bin Zhu","orcid":"https://orcid.org/0000-0003-2297-0828"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Bin Zhu","raw_affiliation_strings":["Department of Information Engineering, University of Padova, Padua, Italy"],"raw_orcid":"https://orcid.org/0000-0003-2297-0828","affiliations":[{"raw_affiliation_string":"Department of Information Engineering, University of Padova, Padua, Italy","institution_ids":["https://openalex.org/I138689650"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I138689650"],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":0.3945,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.59053806,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"65","issue":"7","first_page":"4634","last_page":"4639"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.20569999516010284,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.20569999516010284,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.12229999899864197,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.12099999934434891,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/moment-problem","display_name":"Moment problem","score":0.6251999735832214},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.6039000153541565},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.6004999876022339},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5393000245094299},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.47110000252723694},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.426800012588501},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.4165000021457672},{"id":"https://openalex.org/keywords/multivariable-calculus","display_name":"Multivariable calculus","score":0.3984000086784363},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.37790000438690186}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8334000110626221},{"id":"https://openalex.org/C4285052","wikidata":"https://www.wikidata.org/wiki/Q3406268","display_name":"Moment problem","level":3,"score":0.6251999735832214},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.6039000153541565},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.6004999876022339},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5393000245094299},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.47110000252723694},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4480000138282776},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44190001487731934},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.426800012588501},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.4165000021457672},{"id":"https://openalex.org/C117312493","wikidata":"https://www.wikidata.org/wiki/Q2035437","display_name":"Multivariable calculus","level":2,"score":0.3984000086784363},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.37790000438690186},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.3734000027179718},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.3610000014305115},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.3449999988079071},{"id":"https://openalex.org/C61062188","wikidata":"https://www.wikidata.org/wiki/Q835065","display_name":"Second moment of area","level":2,"score":0.336899995803833},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.3366999924182892},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.33640000224113464},{"id":"https://openalex.org/C89735579","wikidata":"https://www.wikidata.org/wiki/Q6795894","display_name":"Maximum entropy spectral estimation","level":3,"score":0.3183000087738037},{"id":"https://openalex.org/C158457486","wikidata":"https://www.wikidata.org/wiki/Q17104301","display_name":"Multidimensional systems","level":2,"score":0.30399999022483826},{"id":"https://openalex.org/C151424130","wikidata":"https://www.wikidata.org/wiki/Q17123911","display_name":"Stationary ergodic process","level":4,"score":0.27880001068115234},{"id":"https://openalex.org/C196298200","wikidata":"https://www.wikidata.org/wiki/Q577705","display_name":"Critical point (mathematics)","level":2,"score":0.27869999408721924},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27230000495910645},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.2718000113964081},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.27090001106262207},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.2671000063419342},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.26010000705718994},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.25380000472068787}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2019.2903129","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2019.2903129","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1805.12060","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1805.12060","pdf_url":"https://arxiv.org/pdf/1805.12060","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1805.12060","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1805.12060","pdf_url":"https://arxiv.org/pdf/1805.12060","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G955537433","display_name":null,"funder_award_id":"201506230140","funder_id":"https://openalex.org/F4320322725","funder_display_name":"China Scholarship Council"}],"funders":[{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1002571660","https://openalex.org/W1534388827","https://openalex.org/W1685862830","https://openalex.org/W1991286145","https://openalex.org/W2010730829","https://openalex.org/W2017754977","https://openalex.org/W2030352323","https://openalex.org/W2031149397","https://openalex.org/W2045463928","https://openalex.org/W2055607916","https://openalex.org/W2070896621","https://openalex.org/W2101918153","https://openalex.org/W2102762459","https://openalex.org/W2103637013","https://openalex.org/W2105139914","https://openalex.org/W2106525189","https://openalex.org/W2107561939","https://openalex.org/W2109108213","https://openalex.org/W2119127629","https://openalex.org/W2125327144","https://openalex.org/W2125368842","https://openalex.org/W2132328168","https://openalex.org/W2133186968","https://openalex.org/W2141844446","https://openalex.org/W2143135249","https://openalex.org/W2165694945","https://openalex.org/W2168088676","https://openalex.org/W2170060163","https://openalex.org/W2186590998","https://openalex.org/W2759246745","https://openalex.org/W2963999910","https://openalex.org/W2964052428","https://openalex.org/W2964225617","https://openalex.org/W4210921079","https://openalex.org/W6609825543","https://openalex.org/W7070413882"],"related_works":[],"abstract_inverted_index":{"Matrix-valued":[0],"covariance":[1],"extension":[2],"and":[3,17],"multivariate":[4],"spectral":[5,44],"estimation":[6],"are":[7],"formulated":[8],"as":[9],"generalized":[10],"moment":[11,36,55,98],"problems":[12],"in":[13,27,52,79],"the":[14,28,32,54,71,86,97],"\u201cTHREE\u201d":[15],"approach":[16],"its":[18],"extensions.":[19],"Under":[20],"this":[21],"context,":[22],"we":[23,48,82],"discuss":[24],"Theorem":[25],"6":[26],"title":[29],"paper":[30],"concerning":[31],"bijectivity":[33],"of":[34,43],"a":[35,40,50,63,67,91],"map":[37,56,99],"defined":[38],"over":[39],"parametric":[41],"family":[42],"densities.":[45],"In":[46],"particular,":[47],"provide":[49],"counterexample":[51],"which":[53,70,94],"under":[57],"consideration":[58],"is":[59,90,100],"shown":[60],"to":[61],"have":[62],"critical":[64,88],"point,":[65,93],"namely":[66],"point":[68,89],"at":[69],"Jacobian":[72],"loses":[73],"rank.":[74],"Then,":[75],"with":[76],"standard":[77],"techniques":[78],"bifurcation":[80,92],"theory,":[81],"conclude":[83],"further":[84],"that":[85,96],"computed":[87],"means":[95],"not":[101],"injective.":[102]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2019-03-11T00:00:00"}
